That's an interesting idea Fred. If I understand you correctly, you're proposing creating branch points where there's more than one choice for an adjacent tile (which doesn't occur for periodic tilings). It sounds difficult. I suppose for each new tile you could create branches for each set of possible adjacent tiles. One difficulty is that, proceeding in this manner, it is possible to create dead-end configurations that don't tile the entire plane. Perhaps using the inflation rules might be more deterministic. You'd just need to look at a large enough area to ensure that you've found every possible pattern radiating from a given starting configuration. Tom Fred Lunnon writes:
Has anybody considered coordination trees (as it were) for aperiodic tilings (sic --- prefer quasi-crystallographic!), such as planar Penrose rhombs and its generalisations to solid honeycombs?
I gather that these might be of interest to crystallographers, without understanding details of the applications.
WFL
On 1/6/20, Tom Karzes <karzes@sonic.net> wrote:
Neil, do you have coordination sequences for all of the Platonic/Archimedean/Catalan solids? Those seem like the most fundamental ones for polyhedra. I could probably generate them without too much trouble if needed.
Tom